A team has finished a game with 0-3-8 runs-hits-errors line 4 times since 1897, most recently New York Black Yankees on 16 July 1944. That is about one every 110,751 team-games.
Box score for the most recent one ↗
0-3-4 0-3-3 0-3-2 0-3-6 0-3-5 0-3-7 0-3-8 0-4-1 0-4-3 0-4-2 0-4-0 0-4-5 0-4-8
The whole distribution — Runs-Hits-Errors Lines · All 18 shapes